That function is provided by a bit of JavaScript which appears in the markup just below the button. In order:
– ensure JavaScript is enabled in your browser;
– bring up the console (Chrome: control-shift-j) and check for JavaScript errors;
– possible conflict with other plugins: deactivate all plugins except WC, if the problem resolves, reactivate plugins one-by-one to try to identify which one is causing the conflict;
– possible incomplete or corrupted WC install; (a re-install may lose settings though not products)
– possible theme issue: ensure your theme is up-to-date. Temporarily switch to the default TwentyFourteen theme, if the problem resolves the contact your theme provider;
– please post the link to your site.